Remark 1 theo2 shows that each node in algcon1 exactly converges to the average at the linear rate \(\mathcal {O}(\frac{1}{(1-\delta )\rho }\log \frac{1}{\epsilon })\) , which strictly improves the rate \(\mathcal {O}(\frac{1}{(1-\delta )\rho ^2}\log \frac{1}{\epsilon })\)  in [1]}, and recovers the best rate of algcon3 in terms of \(\rho \)[2]}. Moreover, theo2 shows the linear convergence of both innovations and consensus errors to zero, which is consistent with our observations.

